After five days of injections of filgrastim, a medicine to stimulated the growth of white blood cells, patients undergo apheresis or bone marrow harvesting, or both, to collect stem cells for later re-infusion. For apheresis, whole blood is collected through a needle in an arm vein and circulated through a cell-separating machine where the stem cells are extracted. The rest of the blood is returned through the same needle or a needle in the other arm. Bone marrow harvesting is done under general anesthesia. Stem cells are collected through a large needle inserted into the hipbone.-Patients' immune system cells and bone marrow function are eliminated with chemotherapy (7 days) and total body irradiation (3 days) so the patient's immune system cells will not fight the tumor-fighting cells they are given in treatment.